%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL041-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:06:38 PM UTC 2026
% Result : Unsatisfiable 0.55s 0.83s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 13 unt; 0 nHn; 20 RR)
% Number of literals : 29 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL041-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL041-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL041-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
file('LCL041-1.p',unknown),
[] ).
cnf(6,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(not__dfg(u),v),v))),
file('LCL041-1.p',unknown),
[] ).
cnf(7,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(a,implies__dfg(a,b)),implies__dfg(a,b))),
file('LCL041-1.p',unknown),
[] ).
cnf(21,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),v)) ),
inference(res,[status(thm),theory(equality)],[6,1]),
[iquote('0:Res:6.0,1.1')] ).
cnf(26,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),implies__dfg(v,u)),implies__dfg(v,u))),
inference(sor,[status(thm)],[21,3]),
[iquote('0:SoR:21.0,3.0')] ).
cnf(30,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(v,u)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[26,1]),
[iquote('0:Res:26.0,1.1')] ).
cnf(36,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(65,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[36,6]),
[iquote('0:SoR:36.0,6.0')] ).
cnf(69,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[36,2]),
[iquote('0:SoR:36.0,2.0')] ).
cnf(70,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[36,3]),
[iquote('0:SoR:36.0,3.0')] ).
cnf(72,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[30,70]),
[iquote('0:SoR:30.0,70.0')] ).
cnf(77,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[36,72]),
[iquote('0:SoR:36.0,72.0')] ).
cnf(116,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[77,1]),
[iquote('0:Res:77.0,1.1')] ).
cnf(120,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[116,1]),
[iquote('0:Res:116.1,1.1')] ).
cnf(188,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),v))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[120,65]),
[iquote('0:SoR:120.1,65.0')] ).
cnf(1413,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[188,69]),
[iquote('0:SoR:188.0,69.0')] ).
cnf(1434,plain,
$false,
inference(unc,[status(thm)],[1413,7]),
[iquote('0:UnC:1413.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 5 08:35:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.55/0.83
% 0.55/0.83 SPASS V 3.9
% 0.55/0.83 SPASS beiseite: Proof found.
% 0.55/0.83 % SZS status Theorem
% 0.55/0.83 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.83 SPASS derived 1388 clauses, backtracked 0 clauses, performed 0 splits and kept 593 clauses.
% 0.55/0.83 SPASS allocated 77476 KBytes.
% 0.55/0.83 SPASS spent 0:00:00.42 on the problem.
% 0.55/0.83 0:00:00.06 for the input.
% 0.55/0.83 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.83 0:00:00.06 for inferences.
% 0.55/0.83 0:00:00.00 for the backtracking.
% 0.55/0.83 0:00:00.25 for the reduction.
% 0.55/0.83
% 0.55/0.83
% 0.55/0.83 Here is a proof with depth 9, length 20 :
% 0.55/0.83 % SZS output start Refutation
% See solution above
% 0.55/0.83 Formulae used in the proof : condensed_detachment cn_3 cn_18 cn_21 cn_54 prove_cn_30
% 0.55/0.83
%------------------------------------------------------------------------------